ARTICLE IN PRESS
Applied Radiation and Isotopes 62 (2005) 97–107
Basic considerations for Monte Carlo calculations in soil
Lucian Wielopolskia,*, Zhiguang Songb, Itzhak Orionc,
Albert L. Hansona, George Hendreya
a
b
Department of Environmental Sciences, Brookhaven National Laboratory, Bldg. 490-D, Upton, NY 11973, USA
Guangzhou Institute of Geochemistry, State Key Laboratory of Organic Geochemistry, Chinese, Academy of Science,
Guangzhou, 510640, China
c
Nuclear Engineering Department, Ben Gurion University of the Negev, Beer Sheva, Israel
Received 25 September 2003; received in revised form 13 May 2004; accepted 8 June 2004
Abstract
Monte Carlo codes are extensively used for probabilistic simulations of various physical systems. These codes are
widely used in calculations of neutron and gamma ray transport in soil for radiation shielding, soil activation by
neutrons, well logging industry, and in simulations of complex nuclear gauges for in soil measurements. However, these
calculations are complicated by the diversity of soils in which the proportions of solid, liquid and gas vary considerably
together with extensive variations in soil elemental composition, morphology, and density. Nevertheless use of these
codes requires knowledge of the elemental composition and density of the soil and its physical characteristics as input
information for performing these calculations. It is shown that not always all of the soil parameters are critical but
depend on the objectives of the calculations. An approach for identifying soil elemental composition and some
simplifying assumptions for implementing the transport codes are presented.
r 2004 Elsevier Ltd. All rights reserved.
Keywords: Monte Carlo; Soil elements; Neutrons; Gammas; Transport
1. Introduction
The extensive increase in the computational power of
the desktop computers facilitated a widespread use of
Monte Carlo codes for gamma-neutron transport
calculations. These are probabilistic codes that simulate
step-by-step the processes that guide radiation transport
in matter. These codes enable complex system simulations which other-way would be very time consuming,
costly, and occasionally impossible to perform. These
simulations can be performed with an arbitrary degree
of details provided that all the basic data and complete
system description are available. One of these codes is
*Corresponding author. Tel.: +1-631-344-3656; fax: +1631-344-7244.
E-mail address: [email protected] (L. Wielopolski).
the Monte Carlo Neutron Photon (MCNP) transport
code, developed in Los Alamos National Laboratory
(Breismeister, 1993), that has been widely used for
radiation transport in soil. For example, MCNP has
been used for evaluating soil activation, radiation
shielding in soil, well logging industry, and for design
of complex gauges based on nuclear techniques. One
such technique, which gained widespread use, is in situ,
non-destructive, multi-elemental analysis of bulk geological samples using neutrons (Csikai, 1991; Clayton and
Coleman, 1985). MCNP codes require an input file that
contains complete information about the radiation
source, the geometry of the simulated system, and both
the density and the elemental composition of all
materials through which the radiation passes. In
addition the output tallies to be calculated need to be
specified.
0969-8043/$ - see front matter r 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.apradiso.2004.06.003
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Due to high variability and inhomogeneous nature of
soils, special care must be taken when implementing
MCNP simulations. The main contributing factors to
complexity in using MCNP for in-soil calculations are;
(1) soil is a three-phase system in which the solid phase
contains organic and inorganic components, (2) the
liquid phase carries many different solutes depending on
soil mineralogy, (3) the gaseous phase, although
generally ignored, may contain gases that strongly
absorb neutrons, (4) on a micro-scale soil is a highly
inhomogeneous matrix, although on macro scale some
homogeneity and uniformity can be assumed, and (5)
soil density primarily depends on porosity and water
content. These factors are further complicated by the
nature of the geological formation being studied,
weathering conditions, and depth. For example, it is
well established that the composition of a formation at
depth differs significantly from that on the surface.
These factors make it nearly impossible to provide exact
descriptions of the system. Introducing simplifying
assumptions that depend on the degree of accuracy
required by the final objectives of the calculation to
overcome these complexities. However, the validity of
these assumptions must be tested and validated either by
conducting simple experiments or by performing analyses of the sensitivity of the calculations to perturbations in the assumptions.
Two essential parameters required for MCNP calculations are soil density and elemental composition.
These two primary properties, and an assumption about
soil uniformity are pivotal when designing gadgets for
soil moisture and porosity measurements (Gardner et al.,
1971). These properties are also required when gamma
spectroscopy of neutron induced gamma radiation, due
to delayed, prompt, or inelastic neutron interactions, are
used to solve geophysical problems for the well logging
industry (Schweitzer et al., 1993; Grau et al., 1993), or
when performing non-invasive in situ quantitative
analysis of the elements present in soil (Clayton and
Coleman, 1985).
We describe the use of Monte Carlo calculations
applied to modeling inelastic neutron scattering (INS), a
process we are developing as a technique for quantification of carbon in soil. INS analysis of soil carbon can be
carried out rapidly (30–60 min) and does not disturb the
soil column. This permits re-sampling at the identical
spot over time. Each observation provides a value for
approximately 75–100 lb of soil. This is large enough to
average much of the small-scale heterogeneity in soils
(Wielopolski et al., 2000). At present soil carbon is
measured by taking soil samples to the laboratory. This
conventional process of extracting soil cores disrupts the
soil column and the area around the sampling point.
Alternative methods for soil sampling, laser induced
breakdown spectroscopy (LIBS), (Cramers et al., 2001;
Kincade, 2003) and infrared spectroscopy (McCarty
et al., 2002). However, these in situ approaches are
invasive. In the first case, small volumes of about 50 ml
are vaporized and emission spectroscopy is performed in
the second case it is basically surface analysis; these
methods are therefore not comparable to the INS
method. With re-sampling of the identical spot, and
averaging over a relatively large volume, small changes
in soil carbon content may be detected that, using
conventional methods, would be obscured because of
soil heterogeneity. For example, for till no till agriculture (Lal et al., 1999) scanning large areas for carbon
content will be very useful to assess the changes in
carbon content.
2. Soil components
As pointed out the essential soil parameters, in
addition to the geometry, required for Monte Carlo
simulations are the elemental composition and the bulk
density. These are required to calculate the macroscopic
transport cross section for neutrons and gamma radiation, i.e., the probability of interaction with the
individual elements present in the matrix, and the
density is required for finding the number of atoms in
a volume of interest and calculating the range of travel
for the radiation.
However, the variety of soil types and the multiplicity
of their conditions make it but impossible to obtain a
simple parameterization descriptive of all soils. Instead,
a semi-systematic approach is used to describe the
density and composition of the soil surface and/or near
surface, down to about 100 cm. In this region the soil is a
loose mixture resulting from physical and chemical
weathering and biological processes. It is a heterogeneous system consisting of solid minerals, organic
matter, and liquid and gaseous components. The
proportion of each component varies largely from siteto-site and depends on the climate and stage of soil
By volume
By weight
Inorganic
Solids
70- 95%
Solids
>50% v/v
Soil
Soil Air
~25% v/v
Solution
25% v/v
Organic solids
0.45-6%
<<0.05%
H2O
7-30%
Soluble fraction
<1%
Fig. 1. Soil components with fractional distribution by volume
and weight.
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development. For example, water content strongly
depends on the soil porosity and climate, which in turn
affect soil weathering and other processes in the soil.
General proportions of the soil main components are
shown in Fig. 1, those include the three basic phases
namely; solid, liquid and gaseous, in which the solid
phase is further subdivided into inorganic and organic
components and the liquid contains water and solutes.
The relative abundance by volume and by weight of the
different compartments is also indicated in Fig. 1.
2.1. Solid mineral component
Solid minerals in soil may make up to 95% of the soil
material and determine many of the soil properties. The
simplest soil inorganic classification is by particle size
distribution. The simplest method of characterizing soil
solid is granulometric analysis in which soil solid parts
are classified according to the particle size ranges. These
size ranges are; gravel, >2.0 mm, coarse sand, 2.0–
0.2 mm, fine sand 0.2–0.02 mm, silt 0.02–0.002 mm, and
clay, o0.002 mm (US Department. of Agriculture,
1951). Particle-size distribution of soil varies greatly
from place to place and also with depth. For example,
Table 1 shows the size distribution of three common
types of soils in the United States (Barshad, 1964).
Although this classification does not reveal any information about the chemical composition of the soil it
is often an indication of the mineral components in a
well-developed soil. For example, particles with size
larger than 0.01 mm consist mainly of quartz, while
particles smaller than 0.01 mm are by-and-large clay
minerals.
99
Minerals in soil are generally divided as primary and
secondary minerals and they can make up to 99% by
weight of the solid component of the soil. Mineral
abundance would depend on the types of original rocks
on the earth surface and the degree of weathering.
Minerals initially derived from igneous and metamorphic rocks constitute the primary minerals that
decompose during soil formation process into secondary
minerals following a stability order as indicated in
Fig. 2. The mineralogy and crystallographic structure of
these primary and secondary minerals is well defined and
characterized. For example, well developed soils may
contain numerous kinds of minerals, however, they will
be dominated by quarts which might be present in the
50–90% by weight of the sand and coarser silts. In
addition, sodium feldspar, e.g., albite, potassium feldspars and micas, although very resistant to weathering,
may occur in much lesser quantities in soils in temperate
climatic zones. Since the chemical composition of each
mineral is known based on fixed stochiometry, estimates
of the elemental composition of a given soil could be
derived. Partial breakdown of the soil components is
qualitatively depicted in Fig. 3 with additional breakdown of the inorganic solid matter shown in Fig. 4.
Elemental composition of some of the soil minerals is
given in Table 2.
2.2. Organic component
Organic components may make up to 7% of soil
mass. The main source of organic matter in soil is from
biota and metabolic activities in the rhizosphere,
including root growth and natural decay of the root
Table 1
Particle-size distribution of clay and non-clay soils with uniform depth distribution
Depth (in)
% of whole soil
Fine gravel
Greenfield sand
0–15
15–40
40–72
8
9
8
Hannaford Sandy Loam
0–16
8
10–72
8
Montezuma Clay Loam
0–14
—
14–32
—
32–40
—
Sand
Silt
Clayo5 m
Total
Coarse
Medium
Fine
Very Fine
19
13
20
11
12
11
24
23
23
21
24
20
10
12
12
6
6
6
99
99
100
16
16
8
7
18
19
20
19
18
19
11
11
99
99
32.7
35.2
34.8
28.1
29.1
29.0
72
73
73.7
0.0
0.0
0.7
1.3
0.1
0.1
1.2
0.1
1.0
8.7
8.5
8.1
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100
systems, soil heterotrophs and from plant litter on the
surface. Similarly to inorganic matter, soil organic
matter also shows a great deal of variability in its
Olivine
Ca Plagioclase
Hypersthene
Ca-Na Plagioclase
Augite
Na-Ca Plagioclase
Homblende
Biotite Mica
Increasing
Stability to
Weathering
Na Plagioclase
K Feldspar
Muscovite Mica
Quarts
Fig. 2. Stability order of some primary igneous and metamorphic minerals under the surface weathering conditions.
chemical composition. For example, a mature dry plant
tissue consists of: (1) Carbohydrates with sugars and
starches 1–5%, hemicelluloses 10–28%, and cellulose
20–50%, (2) Fats, waxes, tannins, etc., 1–8%, (3) Lignin
10–30%, and (4) Proteins (simple water soluble and
crude proteins) 1–15%. Organic solids often coat or
aggregate with inorganic particles into soil structure and
they constitute most of the carbon in soil. Nitrogen is
also contained in the organic matter and may range
from 0.02% to 0.25% by weight of the soil make-up; it is
about 5% of the total organic matter. Table 3 provides
some general distribution of various chemical components of the living and non-living organic matter in soil;
the elemental composition of the organic matter is given
in Table 4. The composition of the green tissue of high
plants consists of 75% or more of water, 11% of carbon,
10% of organically bonded oxygen, 2% of hydrogen
and about 2% of ash (Sposito, 1989). More detailed
information about the elemental composition of soil
organic matter is presented in Table 3. In soils carbon is
about one seventh of the organic matter content while
nitrogen is about one twentieth, the C/N ratio varies
Primary
Minerals
Inorganic
Solids
Solids
Organic
Solids
Secondary
Minerals
Living Matter
Non-living
Matter
H2O
SOIL
Organic
Colloids
Liquid
Humic Acids
Fulvoacids
Clay
Minerals
Mineral
Colloids
Amorphous
Minerals
Dissolved
Gases
Soil
Air
Main gases:
CO2 (0.1-1%)
N2 (78%)
O2 (10-20%)
Minor gases:
H2S, H2, CH4 SO2,etc.
Fig. 3. Partial breakdown of the soil main components.
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Primary
Minerals
101
Main minerals:
Quarts SiO2
Microcline K(AlSi3O8) (Potassium felds pars)
Albite Na(AlSi3O8) (Sodium felds pars)
Anorthite Ca(Al2Si2O8) ( Calcium felds pars)
Etc.
Minor minerals:
Micas H2KAl3Si3O12
Biotite (H,K)2(Mg,Fe)2(Al,Fe)2Si3O12
Amphiboles Ca(Mg,Fe)2Si4O12
Pyroxenes Ca(Mg,Fe)Mg(Al,Fe)Si2O6
Olivine MgFeSiO4
Pyrite FeS2
etc.
Clay minerals
Kaolinite H2Al2Si2O8. H2O
Montmorillonites Al3.5Mg0.5Si8O20(OH).nH2O
Illites (K0.2)(K0.8)Al4(AlSiO7)O20(OH)4
Allophanes (amorphous clay minerals)
Secondary
Minerals
Carbonates (can be primary and secondary)
Calcite CaCO3
Dolomite (Ca,Mg)(CO3)2
Magnetite MgCO3
Siderite FeCO3
Gypsum CaSO4.2H2O (semiarid, arid regions)
Nitrite Na2CO3.10H2O
etc.
Iron Oxides, Fe2O3(H2O), Fe3O4
Aluminum oxides, Al2O3
Sulfides FeS2
Halogenides (KCl, NaCl)
Nitrates
Phosphates Ca5(PO4)3(OH,F,Cl)
Fig. 4. Partial breakdown of the primary and secondary minerals.
typically from 8:1 to 15:1, (Buckman and Brady, 1969).
Therefore, for a given soil, the knowledge of organic
carbon content is equal to that of organic matter
content. Qualitative breakdown of the organic matter
is shown in Figs. 3 and 5.
2.3. Liquid
Soil water, located in the soil pore space, together
with the dissolved salts, dissolved organic matter, gases
and dispersed substances from various source is defined
as the soil solution. This is the most dynamic constituent
of the soil. Soil solution is not only important in
supplying the nutrients to growing plants but also serves
as the carrier for the elements that exchange among the
different soil components in the various phases. Knowledge of the water content in soil, and more specifically
the amount of hydrogen in soil is important because; (1)
hydrogen will absorb very effectively thermal neutrons
thus reducing the flux and (2) hydrogen is the best
moderator for fast neutrons thus slowing them down
and reducing the depth penetration of the neutrons.
2.4. Air
The gaseous phase in soil occupies the pore space and
is referred to as the soil air. The main constituents of the
soil air are; CO2, H2O (vapor), O2, and N2, while other
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L. Wielopolski et al. / Applied Radiation and Isotopes 62 (2005) 97–107
Table 2
Major elemental content of common soil minerals
Primary Minerals
Secondary Minerals
Minerals
Si
Al
O
Quartz
Microcline
Albite
Anorthite
Pyrite
46.7
30.3
32.1
20.2
9.7
10.3
19.4
53.3
46.0
48.8
46.0
Kaolinite
Montmorillonites
Illites
Carbonate
Iron oxides
Dolomite
Phosphates
22.7
33.6
4.9
Ca
Mg
K
Na
C
S
14.0
8.8
14.4
53.3
25.6
14.2
19.9
19.2
gases such as H2S, H2, CH4, SO2 and many other gases
can be encountered, and their presence will depend on
the soil conditions. Although by volume the soil air
might occupy a large fraction, its contribution to
chemical composition by weight is negligible as indicated in Fig. 1. Although very unlikely, nevertheless,
attention must be paid to whether the soil air contains
strong neutron absorbers such as: B, Li, Cd and Gd,
these gases could affect the MCNP calculation significantly and therefore have to be carefully evaluated even
on trace level, for instance few tens of ppm.
3. Soil density
Soil density, also referred to, as bulk density, Db ; is a
critical soil parameter required for the MCNP calculations. Soil bulk density is defined as the total soil weight
per unit total volume. Inherent in this definition is the
assumption that the soil’s three-phase system has been
homogenized, which is a reasonable assumption as long
as the soil particle sizes are smaller than the neutron or
gamma rays mean free path. The stated importance of
the bulk density is due to the fact that the neutron
macroscopic cross sections and gamma mass attenuation
coefficients depend on it. Thus the bulk density will
affect the reaction rates and penetration depth of
neutrons and gamma radiation. When combined with
the elemental composition of the soil it will also affects
the slowing down process (thermalization) of the fast
neutrons.
Soil density depends on soil morphology, i.e., particle
shape and size distribution, which is characterized
through the porosity parameter, S: Porosity is defined
as the ratio of the nonsolid, pore space divided by the
total space. The pore space may be partially, Pv ; or
completely, Pv ¼ 1; filled with water thus affecting the
soil density, where Pv is defined as the water volume in
51.7
50.4
69.7
48.0
28.0
52.3
1.8
5.5
40.0
21.7
41.2
12.0
13.0
13.0
the pore space divided by the total pore volume. If the
density of the solid matter is assumed to be Ds and that
of the liquid phase Dw ; then the soil bulk density can be
expressed as:
Db ¼ Ds ð1 SÞ þ Dw SPv :
ð1Þ
For simplicity, assuming arbitrarily a density for the
solid and liquid components to be 2 and 1 g/cm3,
respectively, and a range of values between 0 and 1 for
both Pv and S; Eq. (1) is depicted in Fig. 6. However,
more realistic values for these parameters are for Ds ;
2.4–2.7 g/cm3, Dw slightly above 1 g/cm3 because of the
dissolved minerals, porosity 25–50%, and Db 1.2–1.6 g/
cm3 (Frank and Tolgyessy, 1993; Tolgyessy, 1993). The
significance of Eq. 1 is that it does not exhibit sharp
gradients in the bulk density in soil. Those can be
encountered at the interfaces between soil and solid
rocks. However, as long as the volume with substantial
changes in the soil density remains small relative to the
beam size there will be an averaging effect that will
smooth out these sharp discontinuities (Schacklette and
Boerngen, 1984; Bowen, 1979; Miller and Turk, 1951;
The Nanking Institute of Soil Science, 1982).
4. Soil elemental composition
In the scheme that we propose, once the components
of the soil have been identified it is possible, based on the
knowledge of the individual stoichiometries, to derive
the elemental composition of the soil, or at least to
identify the mean concentrations of the major elements
O, Si, Fe, Al, K, and Ca dominate soil elemental
composition that is mainly determined by the minerals.
Occasionally the exact knowledge of an abundance of an
element needs to be replaced with empirical ratios such
as C/H=7.6, C/N=12, C/S=70, C/P=50, C/O=1.87.
If no information about the soil is available then few
ARTICLE IN PRESS
10–30
1–5
10–28
20–50
1–8
1–15
Humic substances are the products of polymerization of all these components, and the ratio of HA/FA varies from 0.14 to 1.96 in various
soils.
10–30
10–30
3–10
50–80
5–15
5–15
30–50
23–30
40.0–47.5
0.7–3.2
1.2–1.6
103
samples of the soil can be subjected for elemental
analysis. An example of results from soil analysis is
shown in Table 5, Soil A for which the density used was
1.59 g/cm3. In this case there was a need to determine
soil activation due to high-energy neutrons, thus trace
level elements were also included. Soil B in Table 5
represents a carbon rich loam soil used by the PEGS5
Monte Carlo code for transport calculations in soil
(Nelson et al.). Median values of world soils (ovendried) are given in Table 5 (Sumner, 2000). Since the true
distribution of the elements in the soil is seldom known a
uniform distribution is frequently assumed although it is
well known that there are sharp gradients in C, N and
Db from the soil surface through the first half-meter of
the soil profile.
5. Sensitivity analysis
Sensitivity analysis enables testing the validity of the
assumptions and or approximations made during the
simulations. Typical assumptions may refer to elemental
composition, homogeneity, or soil density. Introducing
a change, small or large depending on the effect, in the
parameter of interest in the input file and observing the
variations in the results provides information on the
sensitivity of the simulation to this particular parameter.
Large variations in the results are indicative of the
criticality of the given parameter to the overall simulation. There are no clear rules what constitute large or
small variation and it is up to the investigator to make a
judgment call.
For example, when calculating soil activation detailed
elemental composition of the soil is important. The
different activation cross-sections and half-lives for each
element affect the total induced activity and the
subsequent decay rate. This is demonstrated how the
radioactivity is at the end of the irradiation period, short
term, and after cooling time, long term, depends on the
elemental composition of the soil. However, it is also
shown that the neutron penetration in the soil is less
dependent on the elemental composition.
Living matter
(5–25%)
Humic acids
Fulvic acids
Dry plants
Humin
Bacteria
Grass
High plants
6. Results
Non-living
(75–95%)
Cellulose
Lipids (e.g. fats,
waxes, tannins)
Protein
Table 3
Chemical composition of soil organic matter (dry weight percent)
Carbohydrates
Hemi-celluloses
Others Sugars
and Starches
22–30
Lignin
Ash
0.5–1
L. Wielopolski et al. / Applied Radiation and Isotopes 62 (2005) 97–107
We used the MCNP and ORIGEN2-A (Groff, 1997)
codes for soil activation considering the elemental
composition given by Soil A in Table 5. The model
used fast (14 MeV) neutrons with emission rate of 109 n/s
into 4p: The geometry considered was that of an
isotropic point source placed 5 cm above the ground.
The highest total induced activity after 10 h irradiation
was 6.1 104 Ci, which decayed after one hour to
7.9 107 Ci and after one day to 8.6 108 Ci, which
corresponded to about 17 pCi/g and initially consisted
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104
Table 4
Main elemental content of organic components of soil organic matter
Semi/cellulose and sugars
Fatty acids
Waxes
Resin
Enzymes
Protein and amino acids
Lignin and tannin
Humic acids
Fulvic acids
C
H
O
N
44.4
77.5
81.0
80.0
50.0
53.0
62.0
56.2
45.7
6.2
12.0
13.5
11.5
6.7
7.0
6.1
4.7
5.4
49.4
10.5
5.5
9.0
12.4
23.0
31.9
35.5
44.8
12.4
16.0
3.2(0.8–5.5)
2.1(0.9–3.3)
Sugar
Hemicelluloses,
Celluloses,
Chitin
Carbohydrate
Fatty acids, waxes,
resin and hydrocarbons
Lipids
Roots
Protein, amino acidsandenzyme
Lignin and tannin
Living
matter
Bacteria Actinomycetes
Fungi and Algae
Soil
organism
Micro & Me sofauna
Fatty acids,
hydrocarbons
Protein,
amino acids
and enzyme
Other macrofauna
Earthworms
Humic acids,
Humus
85-90%
Fulvic acids
Humin
Non-living
organic
matter
Lower molecular
Simple saccharides,
Fatty acids, amino acids
Alcohols, esters, sugars
Non-specific
humic
substance:
(<10-15% )
S
Large molecular complex:
starch,
protein,
hemicelluloses,
celluloses,
lignin
Waxes and
bitumen
Fig. 5. Partial breakdown of the living and non-living organic matter.
0.8(0.1–1.5)
1.9(0.1–3.6)
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105
Table 5
Elemental soil composition for; Soil A: Local soil chemical analysis at the laboratory, Soil B: Soil composition used in the data set of
the PEGS4 code (Miller and Turk, 1951), and Soil C: is the median value of world soils, The Nanking Institute of Soil Science, 1982
Element
Soil A (% by weight)
Soil B (% by weight)
Soil C (% by weight)
1
0.2100
0.0013
0.0013
0.1950
0.0032
53.0200
0.0046
0.2450
0.0881
1.0960
43.7600
0.0128
0.0108
0.2250
0.1180
0.0005
0.1228
0.0035
0.0029
0.0151
0.7240
0.0007
0.0009
0.0012
0.0058
0.0035
0.0545
0.0540
0.0063
0.0012
0.0029
0.0050
0.0051
0.0037
2.81
—
—
14.43
0.001
49.64
—
0.82
—
8.93
21.32
—
—
0.56
0.54
—
—
—
—
—
0.96
—
—
—
—
—
—
—
—
—
—
—
—
—
—
0.0030
0.0010
2.0000
0.1000
48.8700
0.0200
0.6300
0.5000
7.1000
33.3000
0.0650
0.0100
1.4000
1.3700
0.0007
0.5000
0.0100
0.1000
0.0850
3.8000
0.0008
0.0040
0.0020
0.0100
0.0050
0.0300
0.0500
—
—
0.0006
0.0010
—
0.0005
H
Li
5
B
6
C
7
N
8
O
9
F
11
Na
12
Mg
13
Al
14
Si
15
P
16
Cl
19
K
20
Ca
21
Sc
22
Ti
23
V
24
Cr
25
Mn
26
Fe
27
Co
28
Ni
29
Cu
37
Rb
39
Y
40
Zr
56
Ba
60
Nd
62
Sm
72
Hf
82
Pb
83
Bi
90
Th
3
Bulk Density, Db
Db = Ds(1-S) + DwSPv
Fig. 6. Bulk density variation versus soil porosity and moisture
fraction.
mainly due to activation of Al, Mg, N, Na and F, after
10 days the main activity was due to Ar and Sc. This
might be compared to naturally occurring activity due
primarily to thorium in soils at Long Island, New York,
of 2.0 108 Ci. However, this activity was two orders
of magnitude less than the natural activity of thorium.
Validity of these calculations and their sensitivity to
soil composition were partially tested by comparing the
neutron fluxes obtained when Soil B, in Table 5, was
used versus results obtained when composition of Soil A
was used. Furthermore, while Soil A used the mean
neutron flux in a cell when using soil B the flux crossing
the cell wall was calculated. All the other parameters
were maintained the same. The neutron flux calculations
of the high-energy group (5–14 MeV) as a function
of depth for various water contents are shown in Fig. 7
for both soil compositions. The graph denoted as
Alt. MCNP Calc in Fig. 7 was based on elemental
ARTICLE IN PRESS
L. Wielopolski et al. / Applied Radiation and Isotopes 62 (2005) 97–107
106
Finally, the affect of soil bulk density on the neutron
transport in the soil of the fast energy group was
calculated for densities varying between 0.5–2.0 g/cm3.
The results are shown in Fig. 8.
1.00e-1
1.00e-2
Soil+ 0% Water
Soil+ 10% Water
Soil+ 25% Water
Soil+ 50% Water
100% Water
Alt. MCNP Calc.
1.00e-3
1.00e-4
7. Summary
1.00e-5
1.00e-6
1.00e-7
0
18
36
54
72
90
Depth (cm)
Fig. 7. The neutron flux intensity versus depth in soil for
various soil water content. The solid squares represent
calculation performed with different soil elemental composition.
3.0e-5
Flux (n/cm2/source n)
Thermal Neutron Flux
50% Moisture bw.
25% Moisture bw.
10% Moisture bw.
0.0% Moisture bw.
2.0e-5
1.0e-5
0.0e0
0
20
40
60
80
100
Depth (cm)
Fig. 8. Thermal neutrons flux for various soil moisture content.
composition of Soil A. Although, these neutron fluxes
were calculated by two different and independent groups
for different soil composition and neutron tallies, they
are in general agreement. The large cell size in Alt.
MCNP calculation prevented comparison of results
below 10 cm. The main incentive for this manuscript
pertains to gamma ray spectroscopy resulting from
inelastic neutron scattering, which has threshold energy
at about 4.8 MeV for carbon, thus the interest in neutron
energies above that energy. Nevertheless, whenever the
interest is in thermal neutrons the behavior of thermal
neutrons as a function of soil moisture content is shown
in Fig. 8. It is interesting to observe that the maximum
flux occurs at about 40 cm deep and shifts to lower depth
with increase in the soil moisture content. At 50%
moisture it is about 30 cm. Thus optimization of the
thermal neutron flux at shallower depth would require
some pre-moderation. At 100% water the maximum
occurs at about 3 cm.
In spite of the large variability in the soil parameters
Monte Carlo calculations are widely used in radiation
transport calculations in soil. However, lack of specific
information on soil elemental composition, density, and
density profile that varies with depth in the near surface
layers hinders these calculations. It was pointed out that
the significance of the various parameters on the analysis
actually depends on the objectives of the calculations.
For example, in the near surface layers, 10–15 cm, we
showed in Fig. 9 that the variation in the soil density has
very small effect on the neutron flux. Similarly, we also
showed in Fig. 7 that soil moisture, up to 50% by
weight, has negligible effect on the transport of the fast
neutron energy group. This is mainly due to reduced
elastic scattering cross section of hydrogen at neutron
energies above 1 MeV. However, in Fig 8 the thermal
neutron intensity almost doubles at Dmax ; the peaking
depth of the thermal neutrons, and there is a shift in
Dmax from about 40 cm to about 30 cm, which is due to
increased thermalization. The thermal neutrons are of
interest when considering prompt and delayed gamma
ray spectroscopy following thermal neutron capture,
whereas carbon and oxygen analysis is concern with fast
neutron capture and the resulting inelastic neutron
scattering. It was pointed out that depending on the
objectives of the Monte Carlo calculation a less refined
information might be required. For example, we
examined the sensitivity of the fast neutron transport
in soil for two neutron group and found no dependence
1.0e-1
Relative Neutron Flux (n/cm2)
Flux (n/cm2/source n)
5 - 14 MeV Neutron Transport in Soil
Effect of Soil Density on Fast
(5-15MeV) Neutron Penetration
1.0e-2
Den-1.3, Water 25%
Den-1.7, Water 25%
Density - 1.2
Density - 1.3
Density - 1.5
Density - 1.7
Density - 0.5
Density - 2.0
1.0e-3
1.0e-4
1.0e-5
1.0e-6
1.0e-7
0
20
40
60
80
100
Depth (cm)
Fig. 9. Fast neutron flux distribution as a function of depth in
soil for various soil densities.
ARTICLE IN PRESS
L. Wielopolski et al. / Applied Radiation and Isotopes 62 (2005) 97–107
on water content, Fig. 7, and weak dependence on
density at larger depth. Indicating that precise information is not very critical. On the other hand when soil
activation is of concern detailed elemental information
of the trace level elements is required, as it was shown
for short term and long term soil activation calculations.
An approximate road map has been presented to
arrive for the soil elemental composition at a given site.
Alternatively, if it is critically important, it is possible to
take a soil sample and analyze it for the elemental
composition. However, it is important to keep in mind
to ascertain how representative this soil sample is of the
entire site. Calculations to understand how individual
parameters affect neutron and gamma radiation transport in soil are in progress and will be reported.
Acknowledgements
This work was supported by the US Department of
Energy under contract No. DE-AC02-98CH10886.
References
Barshad, I., 1964. In: Bear, F.E. (Ed.), Chemistry of the Soil.
ACS Monograph Series.
Bowen, H.J.M., 1979. Environmental Chemistry of the
Elements. Academic Press, London.
Breismeister, J.F. (Ed.), 1993. MCNP-A General Purpose
Monte Carlo N-Particle Transport Code Version 4A. Los
Alamos National Laboratory, NM, LA-12625-M.
Buckman, H.O., Brady, N.C., 1969. The Nature and Properties
of Soils 7th Ed.. The Macmillan Company, New York.
Clayton, C.G., Coleman, C.F., 1985. Analysis of neutron flux
distributions generated by source of fast neutrons in a range
of bituminous coals. Int. J. Appl. Radiat. Isot. 36, 757–788.
Cramers, D.A., Ebinger, M.H., Breshears, D.D., Unkefer, P.J.,
Kammerdiener, S.A., Ferris, M.J., Catlett, K.M., Brown,
J.R., 2001. Measuring total soil carbon with laser-induced
breakdown spectroscopy (LIBS). J. Environ. Qual. 30,
2202–2206.
Csikai, J., 1991. Nuclear data for geology and mining. In:
Qaim, S.M. (Ed.), Nuclear Data for Science and Technology. Springer, Berlin, pp. 644–649.
107
Frank, V., Tolgyessy, J., 1993. The chemistry of soil. In:
Tolgyessy, J. (Ed.), Chemistry and Biology of Water, Air
and Soil Environmental Aspects. Elsevier, Amsterdam.
Gardner, R.P., Dunn, W.L., McDougall, F.H. Lippold, W.J.,
1971. Optimization of density and moisture content
measurements by Nuclear Methods. National Cooperative
Highway Research Program, Report 125
Grau, J.A., Schweitzer, J.S., Draxler, J.K., Gatto, H.,
Lauterjung, J., 1993. Elemental Loggng in the KTB
Pilot Hole-I. NaI-based Spectrometry. Nucl. Geophys. 7,
173–187.
Groff, A.G., 1997. ORIGEN2-A A Revised and updated
version of the Oak Ridge Isotope Generation and Depletion
Code. ORNL Report CCC-178.
Kincade, K., 2003. LIBS Leaves the lab for field work in
industry and defense. Laser Focus World 39 (8), 71–80.
Lal, R., Kimble, J.M., Follett, R.F., Cole, C.V., 1999. The
Potential of US Cropland to Sequester Carbon and Mitigate
the Greenhouse Effect. CRC Press LLC, BocaRaton, FC.
McCarty, G.W., Reeves III, J.B., Reeves, V.B., Follett, R.F.,
Kimble, J.M., 2002. Mid-infrared and near-infrared diffuse
reflectance spectroscopy for soil carbon measurement. Soil
Sci. Soc. Am. J. 66, 640–646.
Miller, C.E., Turk, L.M., 1951. Fundamentals of Soil Science.
Chapman&Hall Limited, London.
Nelson, W.K., Hirayama, H., Rogers, D., The EGS4 code
system. http://www.slac.stanford.edu/egs/codes/zip/egs4pc.
zip
Schacklette, H.T., Boerngen, J.G., 1984. Element concentrations in soils and other Superficial material of the
conterminous United States, US Geological Survey Prof.
Paper 1270.
Schweitzer, J.S., Peterson, C.A., Draxler, J.K., 1993. Elemental
Logging with a Germanium Spectrometer in the Continental Deep Drilling Project, IEEE Trans. Nucl. Sci. 40,
920–923.
Sposito, G., 1989. The Chemistry of Soil. Oxford University
Press, Oxford.
Sumner, M.E., 2000. Editor-in-Chief, Handbook of Soil
Science. CRC Press, Boca Raton, London, New York,
Washington, DC., pp B-13-B16.
The Nanking Institute of Soil Science, The soils of China, 1982.
Chinese Academy of Sciences, Science Press, (in Chinese).
Tolgyessy, J., 1993. Air and Soil Environmental Aspects.
Elsevier, Amsterdam.
US Department of Agriculture Handbook No. 18, (1951).
Wielopolski, L., Orion, I., Hendrey, G., Roger, H., 2000. Soil
Carbon Measurements Using Inelastic Neutron Scattering.
IEEE Trans. Nucl. Sci. 47, 914–917.